Question

Suppose x has a distribution with μ = 59 and σ = 15.

(a) If random samples of size n = 16 are selected, can we say anything about the x distribution of sample means? Multiple choice answers.

Yes, the x distribution is normal with mean μ_x = 59 and σ_x = 0.9.

Yes, the x distribution is normal with mean μ_x = 59 and σ_x = 3.75.    

No, the sample size is too small.

Yes, the x distribution is normal with mean μ_x = 59 and σ_x = 15.

(b) If the original x distribution is normal, can we say anything about the x distribution of random samples of size 16? Multiple choice answer.

Yes, the x distribution is normal with mean μ_x = 59 and σ_x = 15.

Yes, the x distribution is normal with mean μ_x = 59 and σ_x = 3.75.  

   No, the sample size is too small.

Yes, the x distribution is normal with mean μ_x = 59 and σ_x = 0.9.

Find P(55 ≤ x ≤ 60). (Round your answer to four decimal places.)

Answer 1

Solution :

Given that,

mean = = 59

standard deviation = = 15

n = 16

a ) = 59

=  ( /n) = (15 / 16 ) = 3.75

Yes, the x distribution is normal with mean μx = 59 and σx = 3.75

b ) P ( 55    60 )

P (55 - 59 / 3.75) ( - /) (60 - 59 / 3.75)

P (-4 / 3.75 z 1 / 3.75 )

P ( - 1.07 z 0.27 )

P ( z   0.27 ) - P ( z   - 1.07 )

Using z table

= 0.6064 - 0.1423

= 0.4641

Probability = 0.4641